See this thread. http://forums.vwvortex.com/zerothread?id=2665283
I had the same problem. I got a thermal fuse from Action Electronics for $1.99 Canadian. Make sure you get the same heat rating as the original. It should be stamped on the side. You can also just buy an new resistor pack from the stealer for $50-60 if you are so inclined.
My resistor pack was (2000 Jetta) mounted on the bottom of the fan housing. I cut the old thermal fuse out, then crimped a new one in. I didn't solder mine in because i couldn't get it hot enough. Even with two soldering irons simultaneously.... I figured crimping was a better option. I didn't want to risk damaging the thermal fuse again.
To prevent this from happening, it's recommended that you start your fan on 1 and let it run for a while before you crank it up when it's cold outside.
If you want to test if this is definitively your issue, you can rig up some kind of jumper so that electricity can bypass the thermal fuse. Only run it long enough to see whether or not your problem went away. The resistors could potentially get hot enough to start a fire.
When thermal fuses fail, sometimes they will work intermittently when they cool down again. To avoid frustration, it's best just to replace them.
Edit: You can probably get at it from under the dash. Check before you tear your whole dash apart.